轴向高速运动梁的热冲击动力学响应及控制

摘要

研究了轴向高速运动、两端自由梁的热冲击下横向振动响应及控制,采用Hamilton原理得到了受热冲击和控制力的轴向运动高速梁的横向振动方程和边界条件.运用修正的伽辽金法得到了求解系统响应的近似方程.数值仿真给出了速度2马赫时,系统的二阶模型在热冲击下的响应,发现响应较大.运用LQR法设计了最优控制器,其中采用加权系数法选择Q,R矩阵,比较了系统的无控制与有控制下的位移响应,结果表明控制效果良好.%The response and control of the transverse vibration of an axially moving free-free beam with high speed subjected to the thermal shock is studied. Considering the thermal shock and the control force, the transverse vibration equation and boundary conditions are formulated by the Hamilton principle. The instant linearized equations are set up based on Galerkin' s method for the approximation solution. Considering the thermal shock, the displacement responses are calculated, where the axially speed is 2 Ma. Then the controller is designed based on LQR method. The optimal Q and it matrices are selected by the weighting coefficient method. The displacement responses for the control method are simulated by a numerical example. The results show that the control method can suppress the transverse vibration effectively.